I have two different models whose solutions in certain cases are virtually identical. For purposes of illustration, I'd like to plot both solutions in the same figure, but after playing around with Opactiy, Dashed, and Thick, the final result still appears simply as overlapping lines.

$\begingroup$I would plot the difference or the (log) ratio. I don't think you can reasonably show the total variation of the functions and their difference on the same plot.$\endgroup$
– mikadoAug 14 '16 at 20:01

3

$\begingroup$@mikado, that is, their absolute or relative difference, or logs thereof. That's usually more informative than trying to overlay two near-identical curves anyway.$\endgroup$
– J. M. is away♦Aug 14 '16 at 22:50

$\begingroup$Well if you really want to create this plot, even though it won't probably be the most informative one, you could use different plot markers for each function. If you can't get the automatic legend, try to construct your own, there should be some possibilities for that. reference.wolfram.com/language/ref/PlotMarkers.html$\endgroup$
– WalyKuAug 15 '16 at 8:50

If you're plotting two very closely overlapping functions, it's usually acceptable to have them drawn over the top of each other. It could even be considered dishonest to manipulate the axes to exaggerate their differences.

$\begingroup$For people who prefer this route: one method I've seen is to have the "background" curve be thicker and of a contrasting color than the "foreground" curve.$\endgroup$
– J. M. is away♦Aug 15 '16 at 6:47

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